Larkspur-Corte Madera: math

The shaded band is this district's normal range. If nothing about how it works changes, nearly every future year should land inside it. Zero means the typical student just meets the state standard. The small numbers under the years are how many students were tested.

Step 1 · Each year's result

For each grade tested, take the average (mean) scale score from the California Department of Education's results file, and subtract the lowest score that counts as "Standard Met" for that grade. That is the grade's distance from standard. Weight each grade by its share of the students tested, then add the grades up. Grades where the state hides the average because ten or fewer students tested are left out entirely.

2015 from sb_ca2015_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	42,069	2484.5	− 2436	48.5	× 150 / 950	7.7
4	42,072	2524.4	− 2485	39.4	× 168 / 950	7
5	42,073	2522.4	− 2528	−5.6	× 159 / 950	−0.9
6	42,076	2553.5	− 2552	1.5	× 165 / 950	0.3
7	42,077	2583.2	− 2567	16.2	× 153 / 950	2.6
8	42,080	2623.2	− 2586	37.2	× 155 / 950	6.1
Sum, rounded to a whole point						23

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	38,901	2487.1	− 2436	51.1	× 176 / 986	9.1
4	38,903	2532.0	− 2485	47	× 153 / 986	7.3
5	38,906	2546.3	− 2528	18.3	× 176 / 986	3.3
6	38,908	2542.8	− 2552	−9.2	× 170 / 986	−1.6
7	38,910	2575.1	− 2567	8.1	× 161 / 986	1.3
8	38,912	2580.9	− 2586	−5.1	× 150 / 986	−0.8
Sum, rounded to a whole point						19

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	39,865	2471.8	− 2436	35.8	× 178 / 1002	6.4
4	39,867	2538.7	− 2485	53.7	× 166 / 1002	8.9
5	39,868	2557.2	− 2528	29.2	× 162 / 1002	4.7
6	39,870	2586.3	− 2552	34.3	× 170 / 1002	5.8
7	39,872	2587.7	− 2567	20.7	× 172 / 1002	3.6
8	39,875	2624.8	− 2586	38.8	× 154 / 1002	6
Sum, rounded to a whole point						35

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	39,891	2490.8	− 2436	54.8	× 161 / 1016	8.7
4	39,894	2541.2	− 2485	56.2	× 176 / 1016	9.7
5	39,895	2557.9	− 2528	29.9	× 180 / 1016	5.3
6	39,898	2588.0	− 2552	36	× 152 / 1016	5.4
7	39,899	2619.6	− 2567	52.6	× 174 / 1016	9
8	39,902	2608.0	− 2586	22	× 173 / 1016	3.7
Sum, rounded to a whole point						42

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	40,050	2509.0	− 2436	73	× 157 / 1017	11.3
4	40,051	2547.4	− 2485	62.4	× 165 / 1017	10.1
5	40,052	2561.0	− 2528	33	× 180 / 1017	5.8
6	40,053	2586.8	− 2552	34.8	× 184 / 1017	6.3
7	40,054	2626.5	− 2567	59.5	× 157 / 1017	9.2
8	40,055	2629.9	− 2586	43.9	× 174 / 1017	7.5
Sum, rounded to a whole point						50

2021 from sb_ca2021_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	39,017	2505.3	− 2436	69.3	× 149 / 966	10.7
4	39,018	2544.4	− 2485	59.4	× 167 / 966	10.3
5	39,019	2565.9	− 2528	37.9	× 145 / 966	5.7
6	39,020	2582.1	− 2552	30.1	× 157 / 966	4.9
7	39,021	2591.4	− 2567	24.4	× 167 / 966	4.2
8	39,022	2619.7	− 2586	33.7	× 181 / 966	6.3
Sum, rounded to a whole point						42

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	39,839	2486.6	− 2436	50.6	× 153 / 928	8.3
4	39,840	2557.0	− 2485	72	× 139 / 928	10.8
5	39,841	2584.4	− 2528	56.4	× 168 / 928	10.2
6	39,842	2590.4	− 2552	38.4	× 147 / 928	6.1
7	39,843	2597.5	− 2567	30.5	× 158 / 928	5.2
8	39,844	2598.9	− 2586	12.9	× 163 / 928	2.3
Sum, rounded to a whole point						43

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	39,892	2487.4	− 2436	51.4	× 138 / 879	8.1
4	39,893	2530.8	− 2485	45.8	× 145 / 879	7.6
5	39,894	2584.3	− 2528	56.3	× 141 / 879	9
6	39,895	2603.2	− 2552	51.2	× 149 / 879	8.7
7	39,896	2620.6	− 2567	53.6	× 154 / 879	9.4
8	39,897	2605.1	− 2586	19.1	× 152 / 879	3.3
Sum, rounded to a whole point						46

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	39,699	2493.8	− 2436	57.8	× 121 / 832	8.4
4	39,700	2534.2	− 2485	49.2	× 131 / 832	7.7
5	39,701	2550.2	− 2528	22.2	× 146 / 832	3.9
6	39,702	2595.6	− 2552	43.6	× 130 / 832	6.8
7	39,703	2632.2	− 2567	65.2	× 151 / 832	11.8
8	39,704	2623.9	− 2586	37.9	× 153 / 832	7
Sum, rounded to a whole point						46

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	39,470	2501.5	− 2436	65.5	× 109 / 791	9
4	39,471	2550.5	− 2485	65.5	× 121 / 791	10
5	39,472	2576.9	− 2528	48.9	× 125 / 791	7.7
6	39,473	2596.8	− 2552	44.8	× 145 / 791	8.2
7	39,474	2639.7	− 2567	72.7	× 139 / 791	12.8
8	39,475	2644.0	− 2586	58	× 152 / 791	11.1
Sum, rounded to a whole point						59

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. 23, 19, 35, 42, 50, 42, 43, 46, 46, 59 → 40.5
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 4 · 2016→2017: 16 · 2017→2018: 7 · 2018→2019: 8 · 2019→2021: 8 · 2021→2022: 1 · 2022→2023: 3 · 2023→2024: 0 · 2024→2025: 13 → average 6.7
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 6.7 × 2.66 = 17.8. Upper limit 58.3, lower limit 22.7.

Why 2.66? It is the standard factor from quality control, the work of Walter Shewhart and W. Edwards Deming. It turns "how much the result typically changes in a year" into "how far it can wander by chance alone".

Years with no result (no state tests were given in spring 2020) are skipped: the year-to-year change runs from the last year with a result to the next one.

Step 3 · Free or reduced-price meals

The share of enrolled students eligible for free or reduced-price meals — for a district, the total across its schools. From 2014–15, 2015–16, 2016–17, 2017–18, 2018–19, 2020–21, 2021–22, 2022–23, 2023–24, 2024–25, 2025–26.